AC=ABsinB=2√5*(√5/5)=2
BC^2=AB^2-AC^2=20-4= 16
BC=4
(2)△ABC is similar to △DPC, and PC:BC=DC:AC.
PC*AC=BC*DC
2x=4DC
x=2DC
△ The area of △ADP is Y=PC*AD/2=x(AC-DC)/2=x(2-DC)/2.
2Y=x(2-DC)
4Y=x(4-2DC)=x(4-x)
y=x-x^2/4=-( 1-x/2)^2+ 1
When x=2, y max = 1.